The goal of a hybrid stochastic simulation varies based on context, however they typically aim to either improve accuracy or reduce computational complexity.
[1] The first hybrid stochastic simulation was developed by Simon Duane at the University of Illinois at Urbana-Champaign in 1985.
Duane's hybrid stochastic simulation was based upon the idea that the two algorithms complemented each other.
The Langevin equation excelled at simulating long-time properties, but the addition of noise into the system created inefficient exploration of short-time properties.
Duane's initial results using this hybrid stochastic simulation were positive when the model correctly supported the idea of an abrupt finite-temperature transition in quantum chromodynamics, which was a controversial subject at the time.
The Dobramysl and Holcman mixed analytical-stochastic simulation model was published in 2018 by Ulrich Dobramysl and David Holcman, from the University of Cambridge and University of Oxford respectively.
This approach is particularly relevant when a Brownian particle evolves in an infinite space.
Otherwise, explicit analytical expressions are used to map the initial point to a distribution located on an imaginary surface around the targets.
This method has many possible applications, including generating gradient cues in an open space and simulating the diffusion of molecules that have to bind to cell receptors.
The algorithm avoids the explicit simulation long trajectories with large excursions and thus it circumvents the need for an arbitrary cutoff distance for the infinite domain.
The algorithm consists of mapping the source position to a half-sphere containing the absorbing windows.
The probability distribution of hitting is obtained by normalizing the integral of the flux.
The choice of the radius R is arbitrary as long as the sphere S(R) encloses all windows with a buffer of at least size
This algorithm can be used to simulate trajectories of Brownian particles at steady-state close to a region of interest.
The Two-Regime Method for reaction–diffusion simulations was created by Mark Flegg, Jonathan Chapman and Radek Erban at the University of Oxford.
[5] It combines molecular-based algorithms with compartment-based approaches at ideal points during calculations to reduce computational cost.
The molecular-based algorithms are great at giving highly accurate detail on localized regions of interest.
Compartment-based models excel at efficient simulations of large regions.
The steps of the algorithm are as follows: Molecules jump between compartments while in region
Many possibilities exist to couple these regions, which can vary based on the purpose of the simulation.